Slides in PDF - of Marcus Hutter

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Marcus Hutter - 28 - Universal Induction & Intelligence Exercise: Envelope Paradox • I offer you two closed envelopes, one of them contains twice the amount of money than the other. You are allowed to pick one and open it. Now you have two options. Keep the money or decide for the other envelope (which could double or half your gain). • Symmetry argument: It doesn’t matter whether you switch, the expected gain is the same. • Refutation: With probability p = 1/2, the other envelope contains twice/half the amount, i.e. if you switch your expected gain increases by a factor 1.25=(1/2)*2+(1/2)*(1/2). • Present a Bayesian solution.
Marcus Hutter - 29 - Universal Induction & Intelligence Notation: Strings & Probabilities Strings: x=x 1 x 2 ...x n with x t ∈X and x 1:n := x 1 x 2 ...x n−1 x n and x
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